Exponent example 2 (video) | Exponents | Khan Academy (2024)

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  • Eduardo Arzate

    12 years agoPosted 12 years ago. Direct link to Eduardo Arzate's post “Why is it 1 if the expone...”

    Why is it 1 if the exponent is 0?

    (80 votes)

    • Milad Mehri

      9 years agoPosted 9 years ago. Direct link to Milad Mehri's post “The zero exponent is equa...”

      The zero exponent is equal to 1 to satisfy a certain case in manipulating bases with exponents. When multiplying or dividing the same base with exponents we add or subtract the exponents:

      To find the value of (3^3)(3^2) [the short form of (3 X 3 X 3) X (3 X 3) or (27)(9)] we add exponents to get 3^(3+2) or 3^5 with a value of 243.

      To find the value of (3^3)/(3^2)[the short form of (3X3X3)/(3X3) or 27/9] we subtract exponents to get 3^(3-2) or 3^1 with a value of 3.

      Now let us consider the case in which the two exponents are the same:

      To find the value of (3^3)/(3^3) [the short form of (3X3X3)/(3X3X3) or 27/27 we subtract exponents to get 3^(3-3) or 3^0 whose value must equal the value of 27/27, or 1. To make the equation true 3^0 must equal 1.

      The general case is: (x^a)/(x^b)=x^(a-b). When b=a, by substitution, this becomes (x^a)/(x^a)=x^(a-a)=x^0. Now let’s consider it another way. On the left side of the equation we have a division of the same numerator and denominator, which has a value of 1 (anything divided by itself equals 1). On the right side we have x^0. To make the equation true x^0 must equal 1.

      (9 votes)

  • alejandroperez17.cea

    11 years agoPosted 11 years ago. Direct link to alejandroperez17.cea's post “is there a way that someo...”

    is there a way that someone knows how to do this easier

    (7 votes)

  • Lindsey

    11 years agoPosted 11 years ago. Direct link to Lindsey's post “lets say that my problem ...”

    lets say that my problem is 6 to the 8th power. is there a quicker easier way than doing 6*6*6*6*6*6*6*6 but not memory?

    (8 votes)

    • Ohad

      11 years agoPosted 11 years ago. Direct link to Ohad's post “Yes, there is.What is 6 ...”

      Yes, there is.
      What is 6 times 6? That's just 36, or 6^2.
      36^4 is equal to 6^8.
      Now, what is 36 times 36? That's 1296.
      1296^2= 6^8
      Now, we just have to multiply 1296 by itself.
      The result is 1,679,616.

      (9 votes)

  • Bill Rough

    11 years agoPosted 11 years ago. Direct link to Bill Rough's post “I'm just wondering about ...”

    I'm just wondering about the phrasing of exponents. At :23 seconds in the video, the way it is phrased is that 6 is multiplied by itself 8 times. That does not seem quite correct to me. 6^8th power multiplies 6 by 6 only 7 times and once by 1 times. Just being a stickler for words and their meaning but am I missing something? In other words, we start 1x6 and then x6x6x6x6x6x6x6. In short, the first 6 is simply six by itself not times 6, but fine, times one. Does this make sense or no?

    (6 votes)

  • Sajiya70

    8 years agoPosted 8 years ago. Direct link to Sajiya70's post “I was practicing some pro...”

    I was practicing some problems about the Pythagorean Theorem and started off with the basics.
    I know how to solve this problem, but when I checked their method, they did a different kind of simplification that I didn't understand.

    I got to this point:

    ((17^2) - (8^2))

    But, instead just simplifying the powers and subtracting directly, they did this:
    ((17^2) - (8^2)) = (17 + 8) * (17 - 8)

    I know that their way is also right because we both got the same answer of 225.

    All I want to know is how they got from this:

    ((17^2) - (8^2))

    To this:
    (17 + 8) * (17 - 8)

    Thanks so much for taking the time to read this, I really appreciate it!

    (4 votes)

    • Richard Liu

      8 years agoPosted 8 years ago. Direct link to Richard Liu's post “Oh I get what you mean, i...”

      Oh I get what you mean, it's something we call difference of squares . Here's the fundamental principle used:
      x^2 - y^2 = (x + y)(x - y)
      In this case, x = 17 and y = 8, it's just something you can memorize to make life easier!
      It's one of the multiple ways you can factor a quadratic, it's also very commonly seen.
      Hope this helped :)
      Happy holidays!!

      (4 votes)

  • lishaleo3

    a year agoPosted a year ago. Direct link to lishaleo3's post “6^8 = 1679616. precisely ...”

    6^8 = 1679616. precisely like wow that's huge!

    (5 votes)

    • Jude 1:24-25 😊📖

      6 months agoPosted 6 months ago. Direct link to Jude 1:24-25 😊📖's post “Yeah, no kidding!”

      Yeah, no kidding!

      (1 vote)

  • Carla McConnell

    12 years agoPosted 12 years ago. Direct link to Carla McConnell's post “At 0:16 why are there so ...”


    Exponent example 2 (video) | Exponents | Khan Academy (19) 0:16

    why are there so many sixes? I'm confused.

    (1 vote)

    • aravind121

      12 years agoPosted 12 years ago. Direct link to aravind121's post “Dear carla.Those 6.6.6 r...”

      Dear carla.
      Those 6.6.6 represents 6X6X6. (multiplication between two numbers can also be denoted with "." instead of "X"). Please watch the video to completely understand about exponents

      (7 votes)

  • nightfall

    10 months agoPosted 10 months ago. Direct link to nightfall's post “OH I get it now!”

    OH I get it now!

    (4 votes)

  • Allan Worrell

    a year agoPosted a year ago. Direct link to Allan Worrell's post “How do you think about fr...”

    How do you think about fractional or decimal exponents such as
    2^0.3 ?

    (3 votes)

    • RumiWaffles

      a year agoPosted a year ago. Direct link to RumiWaffles's post “You would convert it into...”

      You would convert it into a fraction(0.3 = 3/10)
      Then take the numerator and raise the base to it(2^3)
      And you would square the value to the denominator


      As you see its very complex and you'll learn this later on

      (4 votes)

  • leo.lin.2022

    7 years agoPosted 7 years ago. Direct link to leo.lin.2022's post “what is 0 to the 0th powe...”

    what is 0 to the 0th power?

    (2 votes)

    • Shawn

      7 years agoPosted 7 years ago. Direct link to Shawn's post “It is undefined. Why? Thi...”

      It is undefined. Why? Think of it as a paradox:
      When 0 is raised to any number, it is zero
      When any number is raised to the power of 0, it is one
      So when you put those two together, it just doesn't make sense
      So that is why...
      Hope this helps

      (3 votes)

Exponent example 2 (video) | Exponents | Khan Academy (2024)


What are 2 examples of exponents? ›

Examples of Exponent

Here are some examples: 54 = 5 × 5 × 5 × 5 = 625. 35 = 3 × 3 × 3 × 3 × 3 = 243. 142 = 14 × 14 = 196.

What is an example of an exponent with answer? ›

The exponent of a number shows how many times a number is multiplied by itself. For example, 34 means 3 is multiplied four times by itself, that is, 3 × 3 × 3 × 3 = 34, and here 4 is the exponent of 3. Exponent is also known as the power of a number and in this case, it is read as 3 to the power of 4.

What is the answer to 2 with an exponent of 2? ›

Answer and Explanation:

Two to the second power is 4.

What is the answer to 10 exponent 2? ›

But 10x10 equals 100, meaning 10 to the 2nd power is 100.

What is exponent 2 in math? ›

To find x to the power of 2, we can write it in exponent form as x2, where x is base and 2 is power. Power should always be written on top of the base. It means x is multiplied 2 times, that is, (x) × (x) = x2.

What is rule 2 of exponents? ›

The second law states that to divide two exponential functions with the same base, we subtract the exponents. The third law states that in order to raise a power to a new power, we multiply the exponents.

What is an exponent for beginners? ›

An exponent is a positive or negative number or 0 placed above and to the right of a quantity. It expresses the power to which the quantity is to be raised or lowered. In 4 3, 3 is the exponent. It shows that 4 is to be used as a factor three times: 4 × 4 × 4 (multiplied by itself twice).

What is the little 2 exponent? ›

What does ² mean in math? An exponent of 2 is the symbol for squaring a quantity. To square a quantity is to multiply it by itself.

What is the exponent of 2 called? ›

Why is an exponent of 2 called "square?" x*x = x^2 which is known as a square because while we find the area of a square of length x, we write it as x*x or we say x^2. That is the exponential power is known to be a square.

What is the power of 2 answer? ›

The first ten powers of 2 for non-negative values of n are: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, ...

What is 16 as a power of 2? ›

Answer: 16 to the power of 2 is 256.

What is 2 to the exponent 12? ›

Answer: 2 to the power of 12 can be expressed as 212 = 2 × 2 × 2 × … 12 times = 4096.

What are any 2 laws of exponents? ›

The different Laws of exponents are: a^m ×a^n = a^(m+n), a^m /a^n = a^(m-n), (a^m)^n = a^(mn), a^n /b^n = (a/b)^n, a^0 = 1, a^-m = 1/a^m.

Which have an exponent of 2 are called? ›

Answer: Exponents 2 and 3 have special names. Raising a base to a power of 2 is called “squaring” a number. Raising a base to a power of 3 is called “cubing” a number. The inverse of squaring a number is finding the square root of a number.

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